{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Tutorial 8\n",
    "\n",
    "May 11"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Importing the libraries \n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from math import exp"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "## Euler's method\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.1"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def func(t, y): \n",
    "    return (t**2 + 1) \n",
    "      \n",
    "        \n",
    "class Euler():\n",
    "    def __init__(self, t0, y0, h, func=func):\n",
    "        self.t0 = t0\n",
    "        self.y0 = y0\n",
    "        self.h = h\n",
    "        self.func = func\n",
    "  \n",
    "    def euler(self, t): \n",
    "        temp = -0\n",
    "        y = self.y0\n",
    "        t0 = self.t0\n",
    "        while t0 < t: \n",
    "            y = y + self.h * self.func(t0, y) \n",
    "            t0 = t0 + self.h \n",
    "        return(float(y))\n",
    "\n",
    "method = Euler(0, 2, 0.1, func)\n",
    "method.euler(0.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Mid Point"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Midpoint():\n",
    "    def __init__(self, t0, y0, h, func=func):\n",
    "        self.t0 = t0\n",
    "        self.y0 = y0\n",
    "        self.h = h\n",
    "        self.func = func\n",
    "  \n",
    "    def midpoint(self, t): \n",
    "        temp = -0\n",
    "        y = self.y0\n",
    "        t0 = self.t0\n",
    "        while t0 < t: \n",
    "            y = y + self.h * self.func(t0+(self.h/2), y+ (self.h/2)*self.func(t0,y)) \n",
    "            t0 = t0 + self.h \n",
    "        return(float(y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.10025"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "method = Midpoint(0, 2, 0.1, func)\n",
    "method.midpoint(0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Heun's Method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Heun():\n",
    "    def __init__(self, t0, y0, h, func=func):\n",
    "        self.t0 = t0\n",
    "        self.y0 = y0\n",
    "        self.h = h\n",
    "        self.func = func\n",
    "  \n",
    "    def heun(self, t): \n",
    "        temp = -0\n",
    "        y = self.y0\n",
    "        t0 = self.t0\n",
    "        while t0 < t: \n",
    "            y = y + self.h/2 *(self.func(t0,y) +self.func(t0 + self.h, y+ self.h*self.func(t0,y) )) \n",
    "            t0 = t0 + self.h\n",
    "        return(float(y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.1005"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "method = Heun(0, 2, 0.1, func)\n",
    "method.heun(0.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercice 1a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [],
   "source": [
    "def func(t, y): \n",
    "    return (3*y) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sol(t):\n",
    "    return(2* np.exp(3*t))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ts=np.linspace(1, 3, 100)\n",
    "for count, h in enumerate([1,0.9, 0.7,0.4,0.1, 0.01]):\n",
    "    method = Euler(0, 2, h, func)\n",
    "    yeuler = [method.euler(t) for t in ts]\n",
    "    method = Midpoint(0, 2, h, func)\n",
    "    ymid = [method.midpoint(t) for t in ts]\n",
    "    method = Heun(0, 2, h, func)\n",
    "    yheun = [method.heun(t) for t in ts]\n",
    "    ytruth = [sol(t) for t in ts]\n",
    "    plt.xlabel('Time')\n",
    "    plt.plot(ts, yeuler, label=\"Euler h = %0.4f  \" % h, color='#A60628' );\n",
    "    plt.plot(ts, ymid, label=\"Mid point h = %0.4f  \" % h, color='green' );\n",
    "#     plt.plot(ts, yheun, label=\"Mid point h = %0.4f  \" % h, color='blue' );\n",
    "    plt.plot(ts, ytruth, label='Analytic solution', color='black')\n",
    "    plt.legend();\n",
    "    plt.title(\"Euler's Method\");\n",
    "    \n",
    "    \n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Exact solution : 2.6997176151520064\n",
      "Euler : 2.6\n",
      "Mid point : 2.69\n",
      "Heun : 2.69\n"
     ]
    }
   ],
   "source": [
    "h=0.1\n",
    "t=0.1\n",
    "print('Exact solution :', sol(t))\n",
    "method = Euler(0, 2, h, func)\n",
    "print('Euler :', method.euler(t))\n",
    "method = Midpoint(0, 2, h, func)\n",
    "print('Mid point :', method.midpoint(t))\n",
    "method = Heun(0, 2, h, func)\n",
    "print('Heun :' ,method.heun(t))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Exact solution : 3.644237600781018\n",
      "Euler : 3.3800000000000003\n",
      "Mid point : 3.61805\n",
      "Heun : 3.61805\n"
     ]
    }
   ],
   "source": [
    "h=0.1\n",
    "t=0.2\n",
    "print('Exact solution :', sol(t))\n",
    "method = Euler(0, 2, h, func)\n",
    "print('Euler :', method.euler(t))\n",
    "method = Midpoint(0, 2, h, func)\n",
    "print('Mid point :', method.midpoint(t))\n",
    "method = Heun(0, 2, h, func)\n",
    "print('Heun :' ,method.heun(t))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercice 1b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [],
   "source": [
    "def func(t, y): \n",
    "    return (t**2 +1) \n",
    "\n",
    "def sol(t):\n",
    "    return(t**3/3 + t +8/3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Exact solution : 5.291666666666666\n",
      "Euler : 5.0\n",
      "Mid point : 5.28125\n",
      "Heun : 5.3125\n"
     ]
    }
   ],
   "source": [
    "h=0.5\n",
    "t=1.5\n",
    "print('Exact solution :', sol(t))\n",
    "method = Euler(1, 4, h, func)\n",
    "print('Euler :', method.euler(t))\n",
    "method = Midpoint(1, 4, h, func)\n",
    "print('Mid point :', method.midpoint(t))\n",
    "method = Heun(1, 4, h, func)\n",
    "print('Heun :' ,method.heun(t))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Exact solution : 7.333333333333332\n",
      "Euler : 6.625\n",
      "Mid point : 7.3125\n",
      "Heun : 7.375\n"
     ]
    }
   ],
   "source": [
    "h=0.5\n",
    "t=2\n",
    "print('Exact solution :', sol(t))\n",
    "method = Euler(1, 4, h, func)\n",
    "print('Euler :', method.euler(t))\n",
    "method = Midpoint(1, 4, h, func)\n",
    "print('Mid point :', method.midpoint(t))\n",
    "method = Heun(1, 4, h, func)\n",
    "print('Heun :' ,method.heun(t))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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